Answer: x^2 - 2xy + y^2 - 1
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Explanation:
Let z = x-y
So we go from (x-y+1)(x-y-1) to (z+1)(z-1) after replacing "x-y" with "z"
Use the difference of squares rule to get (z+1)(z-1) = z^2 - 1
Now plug in z = x-y and expand using the FOIL rule
z^2 - 1 = (x-y)^2 - 1
z^2 - 1 = (x-y)(x-y) - 1
z^2 - 1 = x^2 - xy - yx + y^2 - 1
z^2 - 1 = x^2 - xy - xy + y^2 - 1
z^2 - 1 = x^2 - 2xy + y^2 - 1
Therefore, (x-y+1)(x-y-1) expands fully out to x^2 - 2xy + y^2 - 1
